# Questions tagged [abstract-algebra]

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6 questions
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### Special elements in the $C^*$ algebra $A \otimes \mathcal{K}$.

Context: Let $A$ be an ungraded (not necessarily unital) $C^*$ algebra. $\mathcal{K}$ space of compact bounded operators on an infinite separable graded Hilbert space $H=H_0 \oplus H_1$. Consider ...
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### Balls and Boxes

Three urns contain marbles. Each urn is large enough to hold all the marbles . The only operation allowed is to move marbles from an urn to another urn, such that the number of marbles in the ...
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### What is the dicyclic group of order $12$? (What is $\mathbb{Z}_3\rtimes \mathbb{Z}_4$)

I have come across the dicyclic group of order $12$. I can see that this is generated by three elements subject to some relations. Is there a way to realize this group without talking about generators ...
Let $\mathbb N = \{0,1,2,\ldots\}$ be the monoid of natural numbers with zero. Suppose $S \subseteq \mathbb N \times \mathbb N$ be some subset such that the number of sets of the form $\{ (i,j) \mid (... 0answers 51 views +50 ### Prime ideals of$R[x]$that intersect$R$in$P$Let$R$be a noetherian ring and$P$a prime ideal of height$h$. Show that the prime ideals$Q\subset R[x]$that intersect$R$in$P$are of the following two kinds, with height as shown:$Q=...
In the nlab article about localization, a side note says When interpreting a ring under Isbell duality as the ring of functions on some space $X$ (its spectrum), […] Unfortunately, the article ...